Optical State Truncation by Projection Synthesis

David T. Pegg; Lee S. Phillips; Stephen M. Barnett

doi:10.1103/PhysRevLett.81.1604

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Optical State Truncation by Projection Synthesis

David T. Pegg¹, Lee S. Phillips², and Stephen M. Barnett^2,3

¹Faculty of Science, Griffith University, Nathan, Brisbane, Q 4111, Australia
²Department of Physics and Applied Physics, University of Strathclyde, Glasgow G4 ONG, Scotland
³NTT Basic Research Laboratories, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-01, Japan

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Phys. Rev. Lett. 81, 1604 – Published 24 August, 1998

DOI: https://doi.org/10.1103/PhysRevLett.81.1604

Abstract

We show how the number-state expansion of an optical state can be truncated so as to leave only its vacuum and one photon components. This can be achieved using a “quantum scissors” device, the operation of which relies on a nonlocal quantum effect.

References (16)

K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993); A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, 71, 3095 (1993); A. S. Parkins, P. Marte, P. Zoller, O. Carnal, and H. J. Kimble, Phys. Rev. A 51, 1578 (1995).
O. Steuernagel, and J. A. Vaccaro, Phys. Rev. Lett. 75, 3201 (1995).
S. M. Barnett and D. T. Pegg, Phys. Rev. Lett. 76, 4148 (1996); L. S. Phillips, S. M. Barnett, and D. T. Pegg (to be published).
B. Baseia, M. H. Y. Moussa, and V. S. Bagnato, Phys. Lett. A 231, 331 (1997).
D. T. Pegg, S. M. Barnett, and L. S. Phillips, J. Mod. Opt. 44, 2135 (1997); D. T. Pegg and S. M. Barnett, in Quantum Communication, Computing and Measurement, O. Hirota, A. S. Holevo, and C. M. Caves (Plenum, New York, 1997), p. 407.
The photon anticorrelation between the two modes and the coherence of the superposition associated with single photon interference were demonstrated in P. Grangier, G. Roger, and A. Aspect, Europhys. Lett. 1, 173 (1986).
See, for example, S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, Oxford, 1997).
S. M. Tan, D. F. Walls, and M. J. Collett, Phys. Rev. Lett. 66, 252 (1991); E. Santos, 68, 894 (1992); S. M. Tan, D. F. Walls, and M. J. Collett, 68, 895 (1992).
This process might be considered as a limited form of teleportation [[10]] in which that part of state $| C 〉$ formed from the vacuum and one photon states is “teleported” to mode $a$ once the message that the experiment has succeeded and the instruction to shift or not shift the phase by $π$ have been given to the recipient of the field in mode $a$ .
C. H. Bennett, G. Brassard, C. Crépeau, R. Josza, A. Peres, and W. K. Wooters, Phys. Rev. Lett. 70, 1895 (1993).
The information lost due to detector inefficiency results in projection onto a mixed state. Details of the generalization of projection synthesis to include detector inefficiency will be given elsewhere.
R. Josza, J. Mod. Opt. 41, 2315 (1994).
D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).
Interference between down converted photons and a coherent field has been demonstrated byJ. G. Rarity, P. R. Tapster, and R. Loudon, Los Alamos preprint server quant-ph/9702032; J. G. Rarity and P. R. Tapster, Philos. Trans. R. Soc. London A 355, 2267 (1997); J. G. Rarity and P. R. Tapster, Quantum Interferometry, F. DeMartini, G. Denardo, and Y. Shih (VCH, Weinheim, 1996); M. Koashi, K. Kono, M. Matsuoka, and T. Hirano, Phys. Rev. A 50, R3605 (1994); M. Koashi, M. Matsuoka, and T. Hirano, 53, 3621 (1996).
D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993); D. T. Smithey, M. Beck, J. Cooper, and M. G. Raymer, Phys. Rev. A 48, 3159 (1993).
We discuss these applications elsewhere. D. T. Pegg, L. S. Phillips, and S. M. Barnett (to be published).

[c1] K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71, 1816 (1993); A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, 71, 3095 (1993); A. S. Parkins, P. Marte, P. Zoller, O. Carnal, and H. J. Kimble, Phys. Rev. A 51, 1578 (1995).

[c2] O. Steuernagel, and J. A. Vaccaro, Phys. Rev. Lett. 75, 3201 (1995).

[c3] S. M. Barnett and D. T. Pegg, Phys. Rev. Lett. 76, 4148 (1996); L. S. Phillips, S. M. Barnett, and D. T. Pegg (to be published).

[c4] B. Baseia, M. H. Y. Moussa, and V. S. Bagnato, Phys. Lett. A 231, 331 (1997).

[c5] D. T. Pegg, S. M. Barnett, and L. S. Phillips, J. Mod. Opt. 44, 2135 (1997); D. T. Pegg and S. M. Barnett, in Quantum Communication, Computing and Measurement, O. Hirota, A. S. Holevo, and C. M. Caves (Plenum, New York, 1997), p. 407.

[c6] The photon anticorrelation between the two modes and the coherence of the superposition associated with single photon interference were demonstrated in P. Grangier, G. Roger, and A. Aspect, Europhys. Lett. 1, 173 (1986).

[c7] See, for example, S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, Oxford, 1997).

[c8] S. M. Tan, D. F. Walls, and M. J. Collett, Phys. Rev. Lett. 66, 252 (1991); E. Santos, 68, 894 (1992); S. M. Tan, D. F. Walls, and M. J. Collett, 68, 895 (1992).

[c9] This process might be considered as a limited form of teleportation [[10]] in which that part of state $| C 〉$ formed from the vacuum and one photon states is “teleported” to mode $a$ once the message that the experiment has succeeded and the instruction to shift or not shift the phase by $π$ have been given to the recipient of the field in mode $a$ .

[c10] C. H. Bennett, G. Brassard, C. Crépeau, R. Josza, A. Peres, and W. K. Wooters, Phys. Rev. Lett. 70, 1895 (1993).

[c11] The information lost due to detector inefficiency results in projection onto a mixed state. Details of the generalization of projection synthesis to include detector inefficiency will be given elsewhere.

[c12] R. Josza, J. Mod. Opt. 41, 2315 (1994).

[c13] D. C. Burnham and D. L. Weinberg, Phys. Rev. Lett. 25, 84 (1970).

[c14] Interference between down converted photons and a coherent field has been demonstrated byJ. G. Rarity, P. R. Tapster, and R. Loudon, Los Alamos preprint server quant-ph/9702032; J. G. Rarity and P. R. Tapster, Philos. Trans. R. Soc. London A 355, 2267 (1997); J. G. Rarity and P. R. Tapster, Quantum Interferometry, F. DeMartini, G. Denardo, and Y. Shih (VCH, Weinheim, 1996); M. Koashi, K. Kono, M. Matsuoka, and T. Hirano, Phys. Rev. A 50, R3605 (1994); M. Koashi, M. Matsuoka, and T. Hirano, 53, 3621 (1996).

[c15] D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993); D. T. Smithey, M. Beck, J. Cooper, and M. G. Raymer, Phys. Rev. A 48, 3159 (1993).

[c16] We discuss these applications elsewhere. D. T. Pegg, L. S. Phillips, and S. M. Barnett (to be published).

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Optical State Truncation by Projection Synthesis

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